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Volumn 13, Issue 2, 2005, Pages 385-398

Global existence results for nonlinear Schrödinger equations with quadratic potentials

Author keywords

Global well posedness; Mehler's formula; Nonlinear Schr dinger equation; Scattering; Strichartz estimates

Indexed keywords


EID: 23844511635     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.385     Document Type: Article
Times cited : (35)

References (24)
  • 3
    • 0036025581 scopus 로고    scopus 로고
    • Remarks on nonlinear Schrödinger equations with harmonic potential
    • R. Carles, Remarks on nonlinear Schrödinger equations with harmonic potential, Ann. Henri Poincaré 3 (2002), no. 4, 757-772.
    • (2002) Ann. Henri Poincaré , vol.3 , Issue.4 , pp. 757-772
    • Carles, R.1
  • 4
    • 0141814240 scopus 로고    scopus 로고
    • Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
    • R. Carles, Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 3, 501-542.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.3 , pp. 501-542
    • Carles, R.1
  • 5
    • 1542282092 scopus 로고    scopus 로고
    • Nonlinear Schrödinger equations with repulsive harmonic potential and applications
    • R. Carles, Nonlinear Schrödinger equations with repulsive harmonic potential and applications, SIAM J. Math. Anal. 35 (2003), no. 4, 823-843.
    • (2003) SIAM J. Math. Anal. , vol.35 , Issue.4 , pp. 823-843
    • Carles, R.1
  • 6
    • 10244274212 scopus 로고    scopus 로고
    • Semiclassical Nonlinear Schrödinger equations with potential and focusing initial data
    • R. Carles and L. Miller, Semiclassical Nonlinear Schrödinger equations with potential and focusing initial data, Osaka J. Math. 41 (2004), no. 3, 693-725.
    • (2004) Osaka J. Math. , vol.41 , Issue.3 , pp. 693-725
    • Carles, R.1    Miller, L.2
  • 7
    • 85019485429 scopus 로고    scopus 로고
    • Nonlinear Schrödinger equations with Stark potential
    • R. Carles and Y. Nakamura, Nonlinear Schrödinger equations with Stark potential, Hokkaido Math. J. 33 (2004), no. 3, 719-729.
    • (2004) Hokkaido Math. J. , vol.33 , Issue.3 , pp. 719-729
    • Carles, R.1    Nakamura, Y.2
  • 8
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • New York University Courant Institute of Mathematical Sciences, New York
    • T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, vol. 10, New York University Courant Institute of Mathematical Sciences, New York, 2003.
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 9
    • 0011576999 scopus 로고
    • Some remarks on the nonlinear Schrödinger equation in the critical case
    • Springer-Verlag, Berlin
    • T. Cazenave and F. Weissler, Some remarks on the nonlinear Schrödinger equation in the critical case, Lect. Notes in Math., vol. 1394, Springer-Verlag, Berlin, 1989, pp. 18-29.
    • (1989) Lect. Notes in Math. , vol.1394 , pp. 18-29
    • Cazenave, T.1    Weissler, F.2
  • 10
    • 84990700842 scopus 로고
    • Microlocal dispersive smoothing for the Schrödinger equation
    • W. Craig, T. Rappeler, and W. Strauss, Microlocal dispersive smoothing for the Schrödinger equation, Comm. Pure Appl. Math. 48 (1995), no. 8, 769-860.
    • (1995) Comm. Pure Appl. Math. , vol.48 , Issue.8 , pp. 769-860
    • Craig, W.1    Rappeler, T.2    Strauss, W.3
  • 11
    • 0039250942 scopus 로고    scopus 로고
    • Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow
    • S.-I. Doi, Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow, Math. Ann. 318 (2000), 355-389.
    • (2000) Math. Ann. , vol.318 , pp. 355-389
    • Doi, S.-I.1
  • 14
    • 51249179626 scopus 로고
    • A construction of the fundamental solution for the Schrödinger equation
    • D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math. 35 (1979), 41-96.
    • (1979) J. Analyse Math. , vol.35 , pp. 41-96
    • Fujiwara, D.1
  • 15
    • 84972584889 scopus 로고
    • Remarks on the convergence of the Feynman path integrals
    • D. Fujiwara, Remarks on the convergence of the Feynman path integrals, Duke Math. J. 47 (1980), no. 3, 559-600.
    • (1980) Duke Math. J. , vol.47 , Issue.3 , pp. 559-600
    • Fujiwara, D.1
  • 16
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • R. T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys. 18 (1977), 1794-1797.
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1
  • 17
    • 51249162728 scopus 로고
    • Symplectic classification of quadratic forms, and general Mehler formulas
    • L. Hörmander, Symplectic classification of quadratic forms, and general Mehler formulas, Math. Z. 219 (1995), no. 3, 413-449.
    • (1995) Math. Z. , vol.219 , Issue.3 , pp. 413-449
    • Hörmander, L.1
  • 19
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), no. 5, 955-980.
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 20
    • 0003936307 scopus 로고    scopus 로고
    • Analysis, second ed.
    • American Mathematical Society, Providence, RI
    • E. H. Lieb and M. Loss, Analysis, second ed., Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001.
    • (2001) Graduate Studies in Mathematics , vol.14
    • Lieb, E.H.1    Loss, M.2
  • 22
    • 0036383355 scopus 로고    scopus 로고
    • Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
    • G. Staffilani and D. Tataru, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations 27 (2002), no. 7-8, 1337-1372.
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.7-8 , pp. 1337-1372
    • Staffilani, G.1    Tataru, D.2
  • 23
    • 0003201639 scopus 로고
    • Singular integrals and differentiability properties of functions
    • Princeton University Press, Princeton, N. J.
    • E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N. J., 1970.
    • (1970) Princeton Mathematical Series, No. 30 , vol.30
    • Stein, E.M.1
  • 24
    • 0000237067 scopus 로고
    • 2-solutions for nonlinear Schrödinger equations and nonlinear groups
    • 2-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcial. Ekvac. 30 (1987), no. 1, 115-125.
    • (1987) Funkcial. Ekvac. , vol.30 , Issue.1 , pp. 115-125
    • Tsutsumi, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.